Simplify; express your answer in exponential form. Assume $p\neq 0, n\neq 0$. $\dfrac{{p^{-1}n}}{{(p^{2}n^{4})^{3}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${p^{-1}n = p^{-1}n}$ On the left, we have ${p^{-1}}$ to the exponent ${1}$ . Now ${-1 \times 1 = -1}$ , so ${p^{-1} = p^{-1}}$ Apply the ideas above to simplify the equation. $\dfrac{{p^{-1}n}}{{(p^{2}n^{4})^{3}}} = \dfrac{{p^{-1}n}}{{p^{6}n^{12}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{-1}n}}{{p^{6}n^{12}}} = \dfrac{{p^{-1}}}{{p^{6}}} \cdot \dfrac{{n}}{{n^{12}}} = p^{{-1} - {6}} \cdot n^{{1} - {12}} = p^{-7}n^{-11}$